Question

Solve the following pair of linear (simultaneous) equations by the method of elimination:

$2x-3y=7$
$5x+y=9$

• A. $x=4$ and $y=1$
• B. $x=1$ and $y=-2$
• C. $x=2$ and $y=-1$
• D. $x=5$ and $y=-4$

Answer 1

The correct option is C $x=2$ and $y=-1$

$2x-3y=7$ ...$\left(1\right)$

$5x+y=9$ ...$\left(2\right)$

Multiplying $\left(2\right)$ by $3$ and adding $\left(1\right)$ and $\left(3\right)$,

$2x-3y=7$ ...$\left(1\right)$

$15x+3y=27$ ...$\left(3\right)$

$17x=34$

$x=2$

Substituting $x=2$ in $\left(1\right)$, we get

$4-3y=7$

$-3y=3$

$y=-1$

So, $x=2,y=-1$